An explicitly uncoupled VMS stabilization finite element method for the time-dependent Darcy-Brinkman equations in double-diffusive convection

In this article, a full explicitly uncoupled variational multiscale (VMS) stabilization finite element method for solving the Darcy-Brinkman equations in double-diffusive convection is proposed. This method introduces three uncoupled VMS treatments for the velocity, the temperature, and the concentration as the postprocessing steps at each time step, respectively. We only need first to solve three full decoupled linear problems and then to solve three full decoupled postprocessing problems. This method is easy to implement because the existing codes can be used. The unconditional stability is proved and the a priori error estimates are derived. A series of numerical experiments are also given to confirm the theoretical analysis and to demonstrate the efficiency of the new method.